 The current and official versions of the course specifications are available on the web at https://www.usq.edu.au/course/specification/current.
Please consult the web for updates that may occur during the year.

# MAT2100 Algebra and Calculus II

 Semester 2, 2022 Online Units : 1 Faculty or Section : Faculty of Health, Engineering and Sciences School or Department : School of Mathematics, Physics & Computing Grading basis : Graded Course fee schedule : https://www.unisq.edu.au/current-students/administration/fees/fee-schedules

## Staffing

Examiner: Dmitry Strunin

## Requisites

Pre-requisite: MAT1102 or MAT1502 or ENM1600 or Students must be enrolled in the following program: MSCN or MEPR or BSED

## Overview

This course follows on directly from MAT1102 Algebra and Calculus I in developing the concepts and techniques of calculus and linear algebra for application to problems in engineering and science, or as a basis for higher study in mathematics.

Module 1 is an introduction to ordinary differential equations (ODEs) and series including direction fields, Euler's method, first order separable ODEs, first and second order linear ODEs with constant coefficients, Taylor and Fourier series. Module 2 covers multivariable calculus including representation of functions of several variables, surfaces and curves in space, partial differentiation, optimisation, directional derivatives, gradient, divergence and curl, line integrals of the 1-st and 2-nd kinds, iterated integrals, Green's theorem. Module 3 extends the linear algebra of MAT1102 Algebra and Calculus 1 to cover eigenvalues and eigenvectors, vector space, bases, dimensions, rank, systems of linear equations, symmetric matrices, transformations, diagonalisation with applications.

## Course learning outcomes

On successful completion of this course students will be able to:

1. Develop and apply mathematical techniques and skills to solve problems essential to further study in sciences or engineering
2. Demonstrate proficiency to interpret and solve basic mathematical problems relevant to this course;
3. Apply mathematical skills to solve authentic science and engineering problems relevant to this course;
4. Effectively communicate mathematical concepts and arguments using appropriate notation

## Topics

Description Weighting(%)
1. Differential Equations and Series: direction fields - first order linear ODEs - Taylor series - Fourier series - Euler's method - second order linear ODEs with constant coefficients. 35.00
2. Multivariable Calculus: curves in space - surfaces in space - functions of several variables - partial differentiation - geometric interpretation of partial derivatives - maxima/minima problems - directional derivatives - vector fields - curl and divergence - line and work integrals - independence of path. 30.00
3. Linear Algebra: linearly independent vectors - systems of linear algebraic equations - eigenvalues and eigenvectors - symmetric matrices. 35.00

## Text and materials required to be purchased or accessed

James, G 2020, Modern Engineering Mathematics, 6th edn, Pearson (Prentice Hall), Harlow.
Study Book (current year), Course MAT2100 3Algebra and Calculus II, USQ Distance and e-Learning Centre, Toowoomba.
(Available on the course StudyDesk.)
Desirable: scientific calculator (non-programmable and non-graphical), Matlab software.